Some Results on Principal Ideals in Unique Factorization Domain

Abstract

In this study, the intersection algebra of two principal ideals of the unique factorization domain is explained. The generators of the intersection algebra of two principal ideals. The important and sufficient conditions are obtained for the said intersection algebra to be finitely generated. It is also shown that intersection algebra of principal ideals in the polynomial ring is a semigroup ring.

Keywords: Unique Factorization Domain (UFD), Principal Ideals, Polynomial Ring, Commutative Algebra, Abelian Group, Monomial Ideals, Quasi Polynomial, Noetherian ring.